You can get custom vent covers water jet cut out of your stone or tile. Here is one company that does it

https://stonecenterinc.com/heat-register-covers/

Is there any way to move or eliminate that particular vent, given that there are vents to each side? Usually if I am designing something that is a feature, I try to relocate anything that I feel interrupts the design.

Particularly if you are doing a minimalist style design, the solutions for minimizing the impact of vents and outlets and other necessary utilities can get awfully expensive., and the cost of just moving it (if possible) may intersect with the esthetic or decorative solution.